Related papers: Switching graphs and Hadamard matrices
In 1989 we proposed to employ Vandermonde and Hankel multipliers to transform into each other the matrix structures of Toeplitz, Hankel, Vandermonde and Cauchy types as a means of extending any successful algorithm for the inversion of…
Given a family of systems, identifying stabilizing switching signals in terms of infinite walks constructed by concatenating cycles on the underlying directed graph of a switched system that satisfy certain conditions, is a well-known…
In 1986, Oliver Pretzel studied the set of orientations of a connected finite graph $G$ and showed that any two such orientations having the same flow-difference around all closed loops can be obtained from one another by a succession of…
We study the problem of reconfiguring odd matchings, that is, matchings that cover all but a single vertex. Our reconfiguration operation is a so-called flip where the unmatched vertex of the first matching gets matched, while consequently…
In light of recent interest in Hadamard diagonalisable graphs (graphs whose Laplacian matrix is diagonalisable by a Hadamard matrix), we generalise this notion from real to complex Hadamard matrices. We give some basic properties and…
Several researchers have recently explored various graph parameters that can or cannot be characterized by the spectrum of a matrix associated with a graph. In this paper we show that several NP-hard zero forcing numbers are not…
We consider the distribution of cycle counts in a random regular graph, which is closely linked to the graph's spectral properties. We broaden the asymptotic regime in which the cycle counts are known to be approximately Poisson, and we…
In this paper, we introduce a matrix for a mixed graph, called the integrated adjacency matrix. This matrix uniquely determines a mixed graph, as long as the indices of the matrix are specified. Additionally, we associate an (undirected)…
The concept of a configuration graph associated to a primitive, aperiodic substitution is introduced in [1] as a convenient graphical representation of the infinite indeterminism of the shift space of the substitution. The main result of…
We present a new method for constructing Hadamard matrices that combines transformer neural networks with local search in the PatternBoost framework. Our approach is designed for extremely sparse combinatorial search problems and is…
In this paper, we illustrate important aspects of the interplay between weighing matrices, $(v,k,\lambda)$-graphs with fixed-point free involutions, and signed graphs with an orthogonal adjacency matrix, which arises from thin divisible…
The traditional adjacency matrix of a mixed graph is not symmetric in general, hence its eigenvalues may be not real. To overcome this obstacle, several authors have recently defined and studied various Hermitian adjacency matrices of…
In this article, we construct bipartite graphs which are cospectral for both the adjacency and normalized Laplacian matrices using partitioned tensor product. This extends the construction of Ji, Gong, and Wang \cite{ji-gong-wang}. Our…
In the graphical calculus of planar string diagrams, equality is generated by exchange moves, which swap the heights of adjacent vertices. We show that left- and right-handed exchanges each give strongly normalizing rewrite strategies for…
This paper deals with stability of discrete-time switched linear systems whose all subsystems are unstable. We present sufficient conditions on the subsystems matrices such that a switched system is globally exponentially stable under a set…
We extend the crossing-change maps between grid complexes, defined by Ozsv\'ath-Szab\'o-Stipsicz, to filtered grid complexes and give a combinatorial formulation of the Alishahi-Eftekhary $\mathfrak{l}(K)$ knot invariant.
In this paper we asymptotically count $d$-regular $k$-uniform hypergraphs on $n$ vertices, provided $k$ is fixed and $d=d(n)=o(n^{1/2})$. In doing so, we extend to hypergraphs a switching technique of McKay and Wormald.
A Hadamard matrix $H$ of order $n$ is a square matrix with entries $\pm 1$ satisfying $HH^T = nI_n$, where $I_n$ is the identity matrix of order $n$. A circulant Hadamard matrix is a Hadamard matrix whose rows are cyclic shifts of one…
We construct Hadamard matrices of orders 4x251 = 1004 and 4x631 = 2524, and skew-Hadamard matrices of orders 4x213 = 852 and 4x631 = 2524. As far as we know, such matrices have not been constructed previously. The constructions use the…
We present a construction of Neumaier graphs with nexus 1, which generalises two known constructions of Neumaier graphs. We also use W. Wang, L. Qiu, and Y. Hu switching to show that we construct cospectral Neumaier graphs. Finally, we show…